// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H
#define EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H

namespace Eigen {

namespace internal {

    template <typename list> struct tensor_static_symgroup_permutate;

    template <int... nn> struct tensor_static_symgroup_permutate<numeric_list<int, nn...>>
    {
        constexpr static std::size_t N = sizeof...(nn);

        template <typename T> constexpr static inline std::array<T, N> run(const std::array<T, N>& indices) { return {{indices[nn]...}}; }
    };

    template <typename indices_, int flags_> struct tensor_static_symgroup_element
    {
        typedef indices_ indices;
        constexpr static int flags = flags_;
    };

    template <typename Gen, int N> struct tensor_static_symgroup_element_ctor
    {
        typedef tensor_static_symgroup_element<typename gen_numeric_list_swapped_pair<int, N, Gen::One, Gen::Two>::type, Gen::Flags> type;
    };

    template <int N> struct tensor_static_symgroup_identity_ctor
    {
        typedef tensor_static_symgroup_element<typename gen_numeric_list<int, N>::type, 0> type;
    };

    template <typename iib> struct tensor_static_symgroup_multiply_helper
    {
        template <int... iia> constexpr static inline numeric_list<int, get<iia, iib>::value...> helper(numeric_list<int, iia...>)
        {
            return numeric_list<int, get<iia, iib>::value...>();
        }
    };

    template <typename A, typename B> struct tensor_static_symgroup_multiply
    {
    private:
        typedef typename A::indices iia;
        typedef typename B::indices iib;
        constexpr static int ffa = A::flags;
        constexpr static int ffb = B::flags;

    public:
        static_assert(iia::count == iib::count, "Cannot multiply symmetry elements with different number of indices.");

        typedef tensor_static_symgroup_element<decltype(tensor_static_symgroup_multiply_helper<iib>::helper(iia())), ffa ^ ffb> type;
    };

    template <typename A, typename B> struct tensor_static_symgroup_equality
    {
        typedef typename A::indices iia;
        typedef typename B::indices iib;
        constexpr static int ffa = A::flags;
        constexpr static int ffb = B::flags;
        static_assert(iia::count == iib::count, "Cannot compare symmetry elements with different number of indices.");

        constexpr static bool value = is_same<iia, iib>::value;

    private:
        /* this should be zero if they are identical, or else the tensor
     * will be forced to be pure real, pure imaginary or even pure zero
     */
        constexpr static int flags_cmp_ = ffa ^ ffb;

        /* either they are not equal, then we don't care whether the flags
     * match, or they are equal, and then we have to check
     */
        constexpr static bool is_zero = value && flags_cmp_ == NegationFlag;
        constexpr static bool is_real = value && flags_cmp_ == ConjugationFlag;
        constexpr static bool is_imag = value && flags_cmp_ == (NegationFlag | ConjugationFlag);

    public:
        constexpr static int global_flags = (is_real ? GlobalRealFlag : 0) | (is_imag ? GlobalImagFlag : 0) | (is_zero ? GlobalZeroFlag : 0);
    };

    template <std::size_t NumIndices, typename... Gen> struct tensor_static_symgroup
    {
        typedef StaticSGroup<Gen...> type;
        constexpr static std::size_t size = type::static_size;
    };

    template <typename Index, std::size_t N, int... ii, int... jj>
    constexpr static inline std::array<Index, N>
    tensor_static_symgroup_index_permute(std::array<Index, N> idx, internal::numeric_list<int, ii...>, internal::numeric_list<int, jj...>)
    {
        return {{idx[ii]..., idx[jj]...}};
    }

    template <typename Index, int... ii>
    static inline std::vector<Index> tensor_static_symgroup_index_permute(std::vector<Index> idx, internal::numeric_list<int, ii...>)
    {
        std::vector<Index> result{{idx[ii]...}};
        std::size_t target_size = idx.size();
        for (std::size_t i = result.size(); i < target_size; i++) result.push_back(idx[i]);
        return result;
    }

    template <typename T> struct tensor_static_symgroup_do_apply;

    template <typename first, typename... next> struct tensor_static_symgroup_do_apply<internal::type_list<first, next...>>
    {
        template <typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args>
        static inline RV run(const std::array<Index, NumIndices>& idx, RV initial, Args&&... args)
        {
            static_assert(NumIndices >= SGNumIndices, "Can only apply symmetry group to objects that have at least the required amount of indices.");
            typedef typename internal::gen_numeric_list<int, NumIndices - SGNumIndices, SGNumIndices>::type remaining_indices;
            initial = Op::run(
                tensor_static_symgroup_index_permute(idx, typename first::indices(), remaining_indices()), first::flags, initial, std::forward<Args>(args)...);
            return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...);
        }

        template <typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args>
        static inline RV run(const std::vector<Index>& idx, RV initial, Args&&... args)
        {
            eigen_assert(idx.size() >= SGNumIndices && "Can only apply symmetry group to objects that have at least the required amount of indices.");
            initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices()), first::flags, initial, std::forward<Args>(args)...);
            return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...);
        }
    };

    template <EIGEN_TPL_PP_SPEC_HACK_DEF(typename, empty)> struct tensor_static_symgroup_do_apply<internal::type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>>
    {
        template <typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args>
        static inline RV run(const std::array<Index, NumIndices>&, RV initial, Args&&...)
        {
            // do nothing
            return initial;
        }

        template <typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args>
        static inline RV run(const std::vector<Index>&, RV initial, Args&&...)
        {
            // do nothing
            return initial;
        }
    };

}  // end namespace internal

template <typename... Gen> class StaticSGroup
{
    constexpr static std::size_t NumIndices = internal::tensor_symmetry_num_indices<Gen...>::value;
    typedef internal::group_theory::enumerate_group_elements<
        internal::tensor_static_symgroup_multiply,
        internal::tensor_static_symgroup_equality,
        typename internal::tensor_static_symgroup_identity_ctor<NumIndices>::type,
        internal::type_list<typename internal::tensor_static_symgroup_element_ctor<Gen, NumIndices>::type...>>
        group_elements;
    typedef typename group_elements::type ge;

public:
    constexpr inline StaticSGroup() {}
    constexpr inline StaticSGroup(const StaticSGroup<Gen...>&) {}
    constexpr inline StaticSGroup(StaticSGroup<Gen...>&&) {}

    template <typename Op, typename RV, typename Index, std::size_t N, typename... Args>
    static inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args)
    {
        return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...);
    }

    template <typename Op, typename RV, typename Index, typename... Args> static inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args)
    {
        eigen_assert(idx.size() == NumIndices);
        return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...);
    }

    constexpr static std::size_t static_size = ge::count;

    constexpr static inline std::size_t size() { return ge::count; }
    constexpr static inline int globalFlags() { return group_elements::global_flags; }

    template <typename Tensor_, typename... IndexTypes>
    inline internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>>
    operator()(Tensor_& tensor, typename Tensor_::Index firstIndex, IndexTypes... otherIndices) const
    {
        static_assert(sizeof...(otherIndices) + 1 == Tensor_::NumIndices,
                      "Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.");
        return operator()(tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices>{{firstIndex, otherIndices...}});
    }

    template <typename Tensor_>
    inline internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>>
    operator()(Tensor_& tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices> const& indices) const
    {
        return internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>>(tensor, *this, indices);
    }
};

}  // end namespace Eigen

#endif  // EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H

/*
 * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
 */
